Mr. Haynes wants to expand his rectangular living room to make room for an indoor theater system. He asks the contractor to make the width of the room 5 feet longer and he wants the length of the room to be 5 feet longer than twice the width. When finished the new room will have a perimeter of 140ft around. The new dimensions of the room will be

Answer:

7 inches

Step-by-step explanation:

5 square + 5 square=50

the square root of 50 is 7.07

7.07 to the nearest whole number is 7

Answer:

7 Inches

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

5² + 5² = c²

50 = c²

[tex]\sqrt{50}[/tex] = c

c = 7.07

ROUND

c = 7 inches

Answer:

1.24 times as intense

Step-by-step explanation:

The intensity of the sound decreases by 24% at construction site from 4:00 p.m. to 1:00 p.m.

Let the function y = f(x).

Then the average rate of change will be

Average rate of change = (y₂ - y₁) / (x₂ - x₁)

On a busy construction site at 1:00 p.m. the sound level is 124 dB, while at 4:00 p.m. it is 100dB.

Then the intense as the sound of the construction site at 4:00 p.m. is the sound at 1:00 p.m. will be

⇒ (100 – 124) / 100

⇒ -0.24

Then the intensity of the sound decreases by 24% at construction site from 4:00 p.m. to 1:00 p.m.

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Answer:

x=100 degree's

Step-by-step explanation:

Its 100 degrees because you add 80 and 20 degrees and because I think they might be called congruent angles.

Answer:

pretty sure it's just 100, just add 80 and 20, angles are opposite of each other.

Answer:

Step-by-step explanation:

Slope: 3/1 (positive: line go uphill)

y-intercept: -5

Place your pencil on the vertical line (y) on -5. Go up 3 units and 1 to the right, repeat and trace the line (actually you only need two points to trace a line)

Answer: D

Step-by-step explanation:

Since it is subtracting x from 20. D tells the change from 20 dollars after buying the notebook or x.

A is 20 + x

B is 20/x

C is 20x or 20 * x

D is 20 - x

Answer:

B

Step-by-step explanation:

you can see the words cut and smaller so that indicates subtraction

[tex](7 + 17 - 14 - 8)q = 14[/tex]

[tex](24 - 22)q = 14[/tex]

[tex]2q = 14[/tex]

Divide both sides by 2

[tex] \frac{2q}{2} = \frac{14}{2} \\ [/tex]

[tex]q = 7[/tex]

There u go...

Have a great day ❤

Two systems of equations are equivalent if they have they have the same solution/solutions.

Hello,

- 10, - 8, 0, 2, 9

The ascending order is always : negative numbers, zero, positive numbers

Answer:

-10, -8, 0, 2, 9

Answer:last one

Step-by-step explanation:

A random number generator picks a number from 6 to 66 in a uniform manner, its resultants are  mathematically given as

Generally, the equation for Mean is mathematically given as

[tex]X=\frac{a+b}{2}\\\\Therefore\\\\X=\frac{6+66}{2}[/tex]

X=36

b)

Generally, the equation for standard deviation is mathematically given as

[tex]\sigma=\sqrt{\frac{b-a}{12}^2}\\\\Therefore\\\\\sigma=\sqrt{(\frac{66-6}{12})^2}\\\\\sigma=\sqrt{25}\\\\[/tex]

[tex]\sigma=5[/tex]

c)

The probability that the number will be exactly 19

[tex]p(x=19)=\frac{19-6}{66-6}[/tex]

p(x=19)=0.2167

d)

The probability that the number will be between 28 and 46 is P(28 < x < 46)

[tex]P(28 < x < 46) =\frac{46-6}{66-6} -(\frac{28-6}{66-6})[/tex]

P(28 < x < 46) =0.3

e)

The probability that the number will be larger than 48 is P(x > 48)

[tex]P(x > 48)=1-P(x\leq 48)[/tex]

Therefore

[tex]P(x > 48)=1-(\frac{48-6}{66-6})[/tex]

P(x > 48)=0.3

f)

[tex]P(x > 17 | x < 62) = P(x\leq 62-P(x leq 17))[/tex]

Therefore

[tex]P(x > 17 | x < 62) =\frac{62-6}{66-6}-(\frac{17-6}{66-6})[/tex]

P(x > 17 | x < 62) =0.75

g)

The 49th percentile

[tex]p(x\leqk=k.(1/66-6))[/tex]

Therefore

[tex]0.49=k*(1/(66-6))[/tex]

k=29.4

h)

The maximum for the lower quartile

P(xl)=h*1/60

0.25=h*1/60

h=15

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Step-by-step explanation:

All angles of the ∆ are same. So it's a equilateral ∆ . So all sides will also be equal .

16 + y = 46

y = 46 -16 = 30

And ,

60 + x + (180-80) = 180

-20 +x = 0

x = 0 +20

x = 20°

Answer:

Given composite function:

Possible functions that compose it:

and

Answer:C.5

Step-by-step explanation:

Answer:

y = -5/2x + 22

Step-by-step explanation:

y = mx + b

2 = -5/2(8) + b

2 = -40/2 + b

2 = -20 + b

22 = b

y = -5/2x + 22

The height  of the skyscraper rounded to the nearest tenth of a meter is

160.0 meters.

The situation will form a right angle triangle.

The angle of elevation is 44 degrees. The horizontal distance of 164

meters from the base of the skyscraper is the adjacent side of the triangle.

Part of the height of the skyscraper is the opposite side of the triangle formed .

Using trigonometric ratio,

tan 44° = opposite / adjacent

tan 44° = h / 164

cross multiply

h = 164 × tan 44°

h = 158.372959068

Recall the angle of elevation was form from his eyes above the ground of

1.62 meters.

Therefore, the height of the skyscraper can be calculated below:

height of the skyscraper = 158.372959068 + 1.62 = 159.992959068

height of the skyscraper ≈ 160.0 meters

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Answer:

n-5=12

This is the answer

The algebraic equation n - 5 = 12 represents the sentence " 5 less than a number is 12" and the solution of the equation is the value of variable n is 17.

Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.

The given statement is "5 less than a number is 12"

According to the given question, translate the phrase into an algebraic form :

⇒ n - 5 = 12

Thus, the algebraic equation n - 5 = 12 represents the sentence " 5 less than a number is 12"

Now the above equation solves for variable n,

⇒ n - 5 = 12

Add 5 to both sides of the above equation,

⇒ n = 12 + 5

⇒ n = 17

Therefore, the algebraic equation n - 5 = 12 represents the sentence " 5 less than a number is 12" and the solution of the equation is the value of variable n is 17.

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Answer:

5.5 hours

Step-by-step explanation:

time = distance/speed

t = 330/60

t = 5.5 hours

Answer:

With discount : $37.76

With tax : $56.38

With both : $40.19

Step-by-step explanation:

Hope this helps

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [tex][x = \frac{-b}{2a}, h(\frac{-b}{2a})][/tex].

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for a and b into the equation to solve for the x-coordinate of the vertex.

[tex]x = \frac{-b}{2a}[/tex]

[tex]x = \frac{-8}{2(1)}[/tex]

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the y-coordinate of the vertex:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

The y-intercept is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

A relation may or may not represent a function.

The costs are given as:

(a) The mapping diagram

To do this, we simply point the number of movies, to the corresponding costs, using arrows

See attachment for the mapping diagram.

(b) Is the relation a function

From the attached mapping, we can see that:

The costs of each movie are different.

This means that: the relation is a function.

(c) Describe the pattern

Notice that as the number of movies increases, the cost also increases;

However, the unit cost decreases.

Hence, the unit cost of each movie decreases as the number of movies increases.

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Answer:

Step-by-step explanation:

Domain: the values that the x cannot be (in this case, the values that make the denominator equal to 0)

x²-5x+6=0

(x-2)(x-3)=0

x≠ 2, 3

in interval notation: (-∞,2)∪(2,3)∪(3,∞)

We just determined that x≠2 or 3 which means that the vertical aysmptotes are

x= 2,3

To find the holes graph both the numerator and denominator then see if anything cancels

2x²+x= x(2x+1)

x²-5x+6= (x-2)(x-3)

because nothing more to do here there are no holes

Answer:

the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in

Step-by-step explanation:

The general area-of-a-triangle formula is A = (1/2)(base)(height), or  = (1/2)bh.

Here b = h + 7.

Applying the area formula given above:  A = 39 in^2 = (1/2)(h + 7)(h), or

78 in^2 = h^2 + 7h,

Rewriting this, in standard quadratic form, we get h^2 + 7h - 78 = 0

                                                                             -7 ± (49 - 4[1][-78])

Applying the quadratic formula to find h:   h = ----------------------------

                                                                                          2

           -7 ± (49 + 312)        -7 ± 19

or h = ----------------------- = ------------- = {-13, 6}

                      2                       2

Discard the negative 13 root; the height must be a positive quantity.

Thus, the height of the triangle is 6 inches and the base is 7 inches greater, or the base is 13 in

Answer:

D. -3

Step-by-step explanation:

g(x) moved 3 units to the right

Answer:

664

Step-by-step explanation:

666 balls to make a full pack

666x3=1998

6000-1998=2

666-2=664

Answer:

X=5/2

4(x+2)2=36

(4x+8)2=36

8x+16=36

8x=36-16

8x=20

X=20/8

X=5/2

Step-by-step explanation:

Hope this helps:)

Answer:

4x + 1

Step-by-step explanation:

evaluating the expression on the left

4(x -3) + 7

Distribute

4x - 12 + 7

4x - 5

Therefor if the constant is any number other than -5

there will be NO SOLUTION

Examples of equations with no solution

4(x -3) + 7 = 4x + 1

4(x -3) + 7 = 4x - 3

4(x -3) + 7 = 4x + 4

Answer:

Step-by-step explanation:

2 rectangles 2.5 x 3.5 and 2 rectangles 2 x 3.5

A = 2(2.5)(3.5) + 2(2.0)(3.5)

A = 7(2.5 + 2.0)

A = 7(4.5)

A = 31.5 cm²